Question: Omar is 3 times as old as Emily. 24 years ago, Omar was 9 times as old as Emily. How old is Omar now?
Answer: We can use the given information to write down two equations that describe the ages of Omar and Emily. Let Omar's current age be $o$ and Emily's current age be $e$ The information in the first sentence can be expressed in the following equation: $o = 3e$ 24 years ago, Omar was $o - 24$ years old, and Emily was $e - 24$ years old. The information in the second sentence can be expressed in the following equation: $o - 24 = 9(e - 24)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $o$ , it might be easiest to solve our first equation for $e$ and substitute it into our second equation. Solving our first equation for $e$ , we get: $e = o / 3$ . Substituting this into our second equation, we get: $o - 24 = 9($ $(o / 3)$ $- 24)$ which combines the information about $o$ from both of our original equations. Simplifying the right side of this equation, we get: $o - 24 = 3 o - 216$ Solving for $o$ , we get: $2 o = 192$ $o = \dfrac{1}{2} \cdot 192 = 96$.